Nonlinear generation of long waves and the reversal of eddy momentum fluxes in a two-layer quasi-geostrophic model

The direction of eddy momentum fluxes in the Earth's midlatitude atmopshere has historically been explained by the interaction between waves and the zonal-mean flow in the quasi-geostrophic theory. While qualitativly adequate in the Earth-like regime, we show that the theory of wave-mean flow interactions becomes less accurate as β or the surface drag decreases. Using a two-layer quasi-geostrophic model of a baroclinic jet on a β-plane, statistically steady states are explored in which the vertically integrated eddy momentum flux is divergent at the center of the jet, rather than convergent as in the Earth-like regime. We show that the divergence is caused by long waves, generated by breaking of short unstable waves near their critical latitudes. Quasi-linear models with no wave-wave interaction can qualitatively capture the Earth-like regime but not the regime with momentum flux divergence at the center of the jet, because the nonlinear wave breaking and long wave generation processes are missing. The fact that the direction of eddy momentum fluxes can be altered by changing parameters in this idealized model challenges our understanding of this central aspect of the general circulation and has implications on the observed reversal of potential vorticity fluxes.